Microscopic Magnetism of A(TiO)Cu4(PO4)4 (A = Ba, Pb, Sr): 31P and 63,65Cu NMR Study

Abstract

We report a comprehensive NMR study of the chiral square-cupola antiferromagnet Pb(TiO)Cu${}_4$(PO${}_4$)${}_4$ and compare its microscopic hyperfine and local-field parameters with the Ba/Sr analogues in the $A$(TiO)Cu${}_4$(PO${}_4$)${}_4$ family. Above $T_{\mathrm{N}}\simeq 6.7$ K, the ${}^{31}$P Knight shift tracks the bulk susceptibility and yields nearly isotropic transferred hyperfine couplings $H_{\mathrm{hf}}^{[010]}=6.77(3)$ and $H_{\mathrm{hf}}^{[001]}=6.19(3)$ kOe/$\hat{I}{¼}_{\mathrm{B}}$. Below $T_{\mathrm{N}}$, the frequency-swept ${}^{31}$P spectrum splits into three lines, in contrast to the four-line pattern reported for BaTCPO. The line separation tracks the onset of the static ${}^{31}$P internal field with a power-law exponent ${\hat{I}}^2\simeq 0.23$, consistent with quasi-two-dimensional criticality. Crystal-rotation ${}^{31}$P NMR in the ordered state resolves all eight symmetry-related P sites and their site-dependent anisotropy. In the ordered state, zero-field ${}^{63,65}$Cu NMR gives a Cu-site internal field $B_{\mathrm{int}}=14.50(6)$ T and a quadrupole frequency $\hat{I}{½}_Q=32.72(5)$ MHz, while point-charge electric-field-gradient calculations including Sternheimer corrections yield an on-site Cu hole occupancy $n_d=0.20(4)$, consistent with a ligand-hole-dominated charge-transfer character. Comparing PbTCPO with BaTCPO and SrTCPO, we find that the transferred hyperfine coupling $H_{\mathrm{hf}}$ varies across the series, reflecting changes in local Cu-O-P covalency, whereas the ordered-state ${}^{31}$P internal field in PbTCPO is $69.5$ mT, considerably higher than in BaTCPO ($35.6$ mT) and SrTCPO ($34.6$ mT). This enhancement is not captured by dipolar terms alone and points to the combined effects of transferred contributions and stacking-dependent cancellation.

13 pages, 11 figures, 5 tables